Weighted \(\overline{\partial}\)-integral representations of \(C^1\)-functions in \(\mathbb C^n\)
type: Item
instance of: scholarly article
title: Weighted \(\overline{\partial}\)-integral representations of \(C^1\)-functions in \(\mathbb C^n\)
zbMATH Open document ID: 1239.32003
DOI: 10.1155/2012/265092
author: Arman H. Karapetyan
published in: Journal of Function Spaces and Applications
publication date: 2012-05-10T00:00:00Z
review text: Summary: For \(C^1\)-functions \(f\) given in the complex space \(\mathbb C^n\), integral representations of the form \[ f = P(f) - T(\overline{\partial}f) \] are obtained. Here \(P\) is the orthogonal projector of the space \[ L^2 \Big\{\mathbb C^n; e^{-\sigma|z|^\rho} |z|^\gamma dm(z)\Big\} \] onto its subspace of entire functions, and the integral operator \(T\) is defined by means of an explicitly constructed kernel \(\Phi\), which is investigated in detail.
Mathematics Subject Classification ID: 32A26
zbMATH DE Number: 6032353
zbMATH Keywords: integral representation
zbMATH Keywords: entire functions
zbMATH Keywords: Fock space
Wikidata QID: Q58908168
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/265092
OpenAlex ID: W2077936699
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description: scientific article; zbMATH DE number 6032353